Related papers: Panphasia: a user guide
This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…
Over the past several decades, unexpected astronomical discoveries have been fueling a new wave of particle model building and are inspiring the next generation of ever-more-sophisticated simulations to reveal the nature of Dark Matter…
We find that, even in the presence of discreteness noise, a Gaussianizing transform (producing a more-Gaussian one-point distribution) reduces nonlinearities in the power spectra of cosmological matter and galaxy density fields, in many…
A few recent works explored incorporating geometric priors to regularize the optimization of Gaussian splatting, further improving its performance. However, those early studies mainly focused on the use of low-order geometric priors (e.g.,…
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
Noise synthesis is a challenging low-level vision task aiming to generate realistic noise given a clean image along with the camera settings. To this end, we propose an effective generative model which utilizes clean features as guidance…
A generator of spatio-temporal pseudo-random Gaussian fields that satisfy the "proportionality of scales" property (Tsyroulnikov, 2001) is presented. The generator is based on a third-order in time stochastic differential equation with a…
Generating dense physical fields from sparse measurements is a fundamental question in sampling, signal processing, and many other applications. State-of-the-art methods either use spatial statistics or rely on examples of dense fields in…
Phenomenologically interesting scalar potentials are highly atypical in generic random landscapes. We develop the mathematical techniques to generate constrained random potentials, i.e. Slepian models, which can globally represent…
Establishing mathematical models is a ubiquitous and effective method to understand the objective world. Due to complex physiological structures and dynamic behaviors, mathematical representation of the human face is an especially…
We present GauStudio, a novel modular framework for modeling 3D Gaussian Splatting (3DGS) to provide standardized, plug-and-play components for users to easily customize and implement a 3DGS pipeline. Supported by our framework, we propose…
A new characterization of random fields appearing in physical models is presented that is based on their well-known Homogeneous Chaos expansions. We take advantage of the adaptation capabilities of these expansions where the core idea is to…
The particle-in-cell numerical method of plasma physics balances a trade-off between computational cost and intrinsic noise. Inference on data produced by these simulations generally consists of binning the data to recover the particle…
We perform cosmological N-body simulations with non-Gaussian initial conditions generated from two independent fields. The dominant contribution to the perturbations comes from a purely Gaussian field, but we allow the second field to have…
This document derives several expected values related to the parameterized mean model with Gaussian noise and their simplified forms.
We present an algorithm that prepares multidimensional Gaussian wavefunctions on qubit arrays and an application of such wavefunctions to multidimensional resampling, a technique useful in quantum digital simulation.
Many aspects of the design trade-off of a space-based instrument and its performance can best be tackled through simulations of the expected observations. The complex interplay of various noise sources in the course of the observations make…
It has been shown that perturbing the input during training implicitly regularises the gradient of the learnt function, leading to smoother models and enhancing generalisation. However, previous research mostly considered the addition of…
Spatial models are used in a variety research areas, such as environmental sciences, epidemiology, or physics. A common phenomenon in many spatial regression models is spatial confounding. This phenomenon takes place when spatially indexed…
The composition of multiple Gaussian Processes as a Deep Gaussian Process (DGP) enables a deep probabilistic nonparametric approach to flexibly tackle complex machine learning problems with sound quantification of uncertainty. Existing…